In the oil and gas industry, seismic prospecting techniques are commonly used in the search for subterranean hydrocarbon deposits. An important step in this search is the construction of an image of a three dimensional (3-D) volume of the subsurface of the earth. In conventional seismic prospecting, the seismic data required to construct that image are acquired along a two dimensional (2-D) grid of shot lines. Typically, this grid lies on the surface of the earth. At each shot point in each line, an energy source generates seismic signals that propagate into the earth and are partially reflected by subsurface reflectors. The reflectors are interfaces between formations having different acoustic impedances and are often important features in the desired image. These reflections are recorded by seismic detectors on or near the surface of the earth or in the overlying body of water. Each line is processed independently, and a skilled interpreter can obtain a picture of the entire 3-D volume covered by the grid from the data associated with the individual lines.
The initial steps involving seismic data acquisition and processing are well known in the art. For each line, data from a multiplicity of source locations are recorded by a multiplicity of receivers. After preprocessing and deconvolution, the data are converted from shot-receiver to midpoint-offset coordinates. This conversion involves generation of Common Depth Point (CDP) gathers in which data from source-receiver combinations with the same midpoint are considered to have come from the same reflection point in the earth (the zero-offset point). The different source-receiver distance traces, referred to as offset traces, in a CDP gather are stacked together after correcting for different travel times to give a stacked trace that is an improved estimate of the zero-offset trace. The zero-offset trace is the trace which would be recorded by a receiver coincident with the source. The estimate is generated because subsequent processing procedures require knowledge of the zero-offset reflection point. However, a consequence of the structural complexity and subsurface seismic velocity variation along a typical seismic line is that the position of the stacked trace as recorded is usually an inaccurate estimate of the correct position of the reflection point. The process of moving the seismic data from the position where the data were recorded to the position from which the data originated is called migration.
With the arrival of modern high-speed digital computers, it is possible to perform the migration of a single line of seismic data (2-D migration) efficiently using accurate mathematical models of the propagation of seismic waves through the earth (2-D wave equation migration). The implicit assumption in 2-D migration is that all reflections originate in a vertical plane (the sagittal plane) passing though the line of acquisition. That assumption is valid only if the direction of the line of acquisition is the same as the dip direction of the reflecting horizon. It is not generally possible to satisfy this condition for all reflecting horizons for all lines in a grid of seismic data.
This limitation of 2-D migration led to the development of 3-D seismic data acquisition techniques in which a closely spaced grid of seismic lines is acquired. Using a 3-D model of seismic velocities in the volume covered by the grid, a 3-D wave equation migration can be performed to give an image of the subsurface. The image is better than the image obtained from 2-D migration because data from the entire 3-D grid of seismic lines is used, and because the assumption that reflections originate from the sagittal plane of the line of acquisition is eliminated.
However, the process of acquiring 3-D data and performing a full 3-D migration is expensive--as much as 100 times more than acquiring and migrating a sparse 2-D grid. In addition, it is not always possible to acquire 3-D data at many locations, such as in urban areas or sites with rough terrain. For these reasons, it is preferable to use a sparse grid of 2-D lines to get a 3-D image of the subsurface whenever possible.
One approach that has been used for migrating a 2-D grid of data is map migration. In this method, reflecting horizons on each of the seismic lines are selected, and a contour map showing reflection times to the horizons is produced by a skilled interpreter. Finally, using a 3-D model of subsurface velocities, the contour maps are migrated to give a 3-D depth map of the various horizons. This three step process is labor-intensive, however, and much of the detailed information that is present in the original seismic data is lost during the migration. Because that detailed information can be important in determining the presence of hydrocarbon reservoirs, difficulties in interpretation of the resulting depth map can result.
In order to preserve this detailed information, approaches have been proposed that use the entire set of seismic data in place of map migration. U.S. Pat. No. 5,079,703 to Mosher and Thompson begins with an irregular 2-D grid and, using a 3-D velocity model, produces migrated data on a regular 3-D grid. For each output point, data from each of the lines in the 2-D grid are migrated twice--first along the line and second at a right angle to it. This process, called D-2D migration, does not produce the same result as a full 3-D migration because incorrect velocities are used in the first migration step. To perform the D-2D migration properly, each of the steps must be carried out using the velocity of the final migrated position of the output point. However, because that position is initially an unknown, the first migration is performed using the velocity of the in-line migrated position. Since this point is generally deeper than the final migrated output point (for a migration velocity that increases with depth), the assumed velocity is too high. This limitation of D-2D migration is well known to practitioners of the art.
U.S. Pat. No. 4,672,545 to Lin and Holloway uses time-dip measurements from 2-D lines to estimate 3-D time-dips. The output is obtained by a linear interpolation, along time-dip surfaces, of data from the surrounding 2-D lines. The result of this procedure is an interpolation-based 3-D data set that can be migrated with a 3-D wave equation migration program. The procedure breaks down in structurally complex areas where more than one time-dip on any line at a given reflection time may be present. Furthermore, after migration the interpreter cannot distinguish reliable measured data from less reliable interpolated data.
U.S. Pat. No. 4,964,097 to Wang, Hanson and Cavanaugh ("Wang") is a method for taking a subset of a grid of 3-D data and producing a 3-D velocity model using 2-D depth images and iterative ray tracing. The ray tracing solves the problem of conflicting dips that arises in methods that rely on linear interpolation. This 3-D velocity model may be the desired product or may be used for a full 3-D migration of the complete grid of 3-D data. Wang does not address the problem of migrating a sparse grid of 2-D data.
From the foregoing, it can be seen that there is a need for a method of 3-D migration of a sparse, possibly irregular, grid of 2-D seismic data that places the seismic horizons in their correct spatial position while retaining the data's detailed structural and stratigraphic information. The present invention satisfies these needs.